Spherical cows are important because they let us abstract away all the complications of the real world and think about underlying principles. But what about when the complications are the point? Then we enter the realm of complex systems — which, interestingly, has its own spherical cows. One such is the idea of a “critical” system, balanced at a point where there is interesting dynamics at all scales. We know a lot about such systems, without approaching anything like a complete understanding just yet.
The Biggest Ideas in the Universe | 23. Criticality and Complexity
And here is the associated Q&A video:
The Biggest Ideas in the Universe | Q&A 23 - Criticality and Complexity
Is there a concept of the entropy of distributions? You said that the central limit theorem proves that it is very easy to get to a normal distribution. Almost no matter what distribution you take, if you pick random samples of it and average them, you’ll get a normal distribution. So that would be an example of a high entropy distribution – it’s very difficult to look at a normal distribution and say what the parent distribution was. Similarly, there are examples of distributions where it’s very easy to say what the parent distribution was (if the “distribution” was a single number, for instance).
Here’s a nice resource on complexity from the Santa Fe Institute where Professor Carroll is an external professor.
https://www.complexityexplorer.org/
Quick erratum: sigma square in the normal distribution! My credence in the greatness of the videos is only marginally lowered…
Yikes! the second to last talk… I bet “penultimate” is a low frequency Ziph number. It has been a wonderful series that I will listen to again.
1. You didn’t mention the 3 body problem and Poincare among others. That’s complexity but not in a statistical way exactly, isn’t it? How has that developed in “n body systems”?
2. Has “complexity” had an impact in QM and cosmology (see #1 above)?
3. The “logistic map” seems to be an important part of the complexity cannon. Do you have a reaction to it?
4. You mentioned the relationship of “entropy” and “complexity” a few times. As an entropy expert, have you explored this area?
IF THE LISTENERS TO THESE TALKS WANTED TO MAKE AT LEAST A ONE TIME MONETARY CONTRIBUTION, HOW WOULD WE DO SO?
Alright, I’ll ask. How do complex structures relate to entropy? Is life an entropy catalyst? Does the entropy of the universe increase faster because we are here?
Thanks for the podcast Sean. Excellent as always.
Given the chemical properties of hydrogen, carbon, oxygen, nitrogen and some metals, has any one done power law analysis and preferential attachment analysis for formation of complex organic molecules, amino acids, proteins, RNA, viruses, DNA and eventually life? is that even applicable to the stated problem. Does the nature of organic chemistry make life an imperative on earth and elsewhere where similar conditions exist?
Has our universe essentially been critical since recombination then? Is everything interesting coming from the phase transition between the early Big Bang and the final heat death of the universe?
As the prime example of complexity emerging from a simple rule I can only think of ‘evolution by natural selection’. Or, how after the start of time random events combined with environmental pressure produced curious minds exploring ‘The biggest ideas of the Universe’.
Love your work.
One definition of complexity is “heterogeneity of the parts of a system”, which, I suppose, includes qualitative differences and not just differences of scale. Isn’t there a level of complexity where no spherical cows are conceivable and the only possible model is the system itself without simplification.
Douglas Adams’ idea of planet Earth as as a giant computer used to model the meaning of life comes to mind.
I notice that the wordpress update has eliminated the edit function. I guess I’ll just have to live with my punctuation mistakes.
I’m wondering what the last Big Idea could possibly be.
It’s amazing how power laws apply to so many different fields! Especially, one should add power law scale invariance in cosmology (power law spectra, correlation functions) and self-similarity of fractals (e.g. Mandelbrot sets and fractal attractors in Chaos Theory).
Greeting Sir
I had a question in my mind…”what would happen if a radio signal of some fixed energy say ‘E’ is shot in space considering that the space is expanding…how far it could go before it dies out…and what would happen to the photons which were carrying that energy??”
Please reply in your free time.
Regards
“Testing”(? )message received.
Can you please make a clarifying comment on Stuart Bartlett’s statement that models of Darwinian evolution show a evolution from complexity to simplicity? I had never heard of this before. Are you aware of such experiments. It is my understanding that in biology Darwinian evolution i.e. random mutation modulated by the natural selection (at each generation consistent with the environment at that time – and the environment itself may change over the full time frame of the evolution) results in complexity from simplicity given that the environment remained within the tolerance band so that complexity could build up. It is true that if Darwinian evolution does not have “simplicity to complexity” as the only vector. It is a special case when the environment remains stable enough over the time frame in questions so that the complexity can build up. I think of this to be somewhat similar to the V shape of entropy (in a quantum fluctuation) you talk about whereby there can be a phase where entropy is going down. Our current universe is a special case and happen to be on the right arm the V where the entropy is increasing.
I thought Theory of Darwinian evolution was a settled science at least to the same level as General Theory of relativity. I think in your podcast you were a very polite host (at some level you should be and are expected to be and you always are) and did not push back more on him to the extent I would have liked. Sorry for the sociological comment, but I feel that the scientific statements without evidence that refute established science need to be pushed back harder. I would put Stuart’s comment closer to flat earth people.
Thank you so much for your generosity and skill in explaining these ideas to someone who is interested but has only a very basic background in physics. It is giving me so much to think about during lockdown and beyond: they simultaneously save my sanity and fry my brain. The talks are one of the few really good things of 2020.
Could we as community create an index of the most significant terms described in each video? It would make easier to search.
f apparent complexity is coarse grained Kolmogorov complexity, that involves a length scale.
If long scale interactions are required for complexity to evolve, that involves a length scale.
Are those length scales related? Are there effects happening at different length scales?